The table you provided shows the data of traffic violations and accidents from 2018 to 2021 in a certain province, as follows:

a. Determining the Regression Line Equation

To establish a regression line equation, we use the formula:

$Y = a + bX$

Where:

• $Y$ is the dependent variable (number of accidents),
• $X$ is the independent variable (number of violations),
• $a$ is the intercept,
• $b$ is the slope of the regression line.

Steps:

1. Calculate the slope $b$ using the formula: $b = \frac{n(\sum XY) - (\sum X)(\sum Y)}{n(\sum X^2) - (\sum X)^2}$

2. Calculate the intercept $a$ using the formula: $a = \frac{\sum Y - b(\sum X)}{n}$

Where $n$ is the number of data points.

b. Estimating the number of accidents in 2022 when the violations are 20,000

After calculating the regression equation from part (a), substitute $X = 20,000$ into the equation to predict the number of accidents.

Let me now perform these calculations.The regression equation is:

$Y = 6159.40 - 0.00457X$

Where:

• $Y$ is the number of accidents,
• $X$ is the number of traffic violations.

a. The regression line equation is:

$Y = 6159.40 - 0.00457X$

b. For 20,000 traffic violations in 2022, the estimated number of accidents would be:

$Y = 6067.95 \text{ accidents}$

This means that, if the number of traffic violations in 2022 is 20,000, the estimated number of traffic accidents is approximately 6068.

Do you need more details or have any questions?

Here are some follow-up questions for further exploration:

1. How can you interpret the negative slope in this context?
2. What are the limitations of using this regression model for future predictions?
3. How does the decrease in violations over time impact accident predictions?
4. Can we expect a similar trend for future years based on this data?
5. What other factors might influence the number of accidents that are not captured by the violations data?

Tip: It's always important to check the strength of the relationship between variables (e.g., through correlation) before making strong conclusions from a regression model.